A small business just leased a new presentation equipment and a color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of
$100 a year plus a $25 service charge for each repair needed. The company's research
Indicates that during a given year 86% of these computers need no repairs, 9% need to be
Repaired once, 4% twice, 1% three times, and none required more than three repairs.
The standard deviation of the company's annual expense with the service contract for the
Presentation equipment is
A) $105.
B) $10.25.
C) $187.42.
D) $13.69.
E) $2.75.

Question

Quizplus · Accepted Answer

To find the standard deviation of the company's annual expense with the service contract, we first calculate the expected value (mean) and then the variance, from which the standard deviation is the square root.Given probabilities and repair costs:- 86% chance of 0 repairs: $100 annual fee only.- 9% chance of 1 repair: $100 + $25 = $125.- 4% chance of 2 repairs: $100 + 2($25) = $150.- 1% chance of 3 repairs: $100 + 3($25) = $175.Expected value (mean) calculation:$$E(X) = (0.86 \times 100) + (0.09 \times 125) + (0.04 \times 150) + (0.01 \times 175) = 86 + 11.25 + 6 + 1.75 = 105$$Variance calculation:$$Var(X) = (0.86 \times (100-105)^2) + (0.09 \times (125-105)^2) + (0.04 \times (150-105)^2) + (0.01 \times (175-105)^2)$$$$Var(X) = (0.86 \times 25) + (0.09 \times 400) + (0.04 \times 2025) + (0.01 \times 4900)$$$$Var(X) = 21.5 + 36 + 81 + 49 = 187.5$$Standard deviation is the square root of variance:$$SD(X) = \sqrt{187.5} \approx 13.69$$Therefore, the correct answer is D) $13.69.

A Small Business Just Leased a New Presentation Equipment and a Color